Although proponents argue that peremptory challenges make juries more impartial by eliminating “extreme” jurors, studies testing this theory are rare and inconclusive. For this article, two formal models of jury selection are constructed, and various selection procedures are tested, assuming that attorneys act rationally rather than discriminate based on animus. The models demonstrate that even when used rationally, peremptory challenges can distort jury decision making and undermine verdict reliability. Peremptory challenges systematically shift jurors toward the majority view of the population by favoring median jurors over extreme jurors. If the population of potential jurors is skewed in favor of conviction - as empirical evidence suggests is usually the case - then peremptory challenges have the unexpected result of making convictions more likely, rather than promoting reasoned deliberation without prejudice to the result. This is troubling when jurisdictions almost universally award more peremptory challenges in trials involving the most serious crimes. And this effect is magnified when attorneys have more complete information about jurors, suggesting the problem may become worse in the future. Moreover, juries selected with more peremptory challenges become more ideologically and demographically homogenous, even when attorneys do not engage in discrimination, reducing the accuracy of jury verdicts. Although this second effect has been seen empirically, the results of the models suggest that it is an inevitable result of the peremptory challenge process rather than an effect of discrimination by attorneys.